**Shearing** deals with changing the shape and size of the 2D object along x-axis and y-axis. It is similar to sliding the layers in one direction to change the shape of the 2D object.It is an ideal technique to change the shape of an existing object in a two dimensional plane. In a two dimensional plane, the object size can be changed along X direction as well as Y direction.

**x-Shear :**

In x shear, the y co-ordinates remain the same but the x co-ordinates changes. If P(x, y) is the point then the new points will be P’(x’, y’) given as –

Matrix Form:

**y-Shear :**

In y shear, the x co-ordinates remain the same but the y co-ordinates changes. If P(x, y) is the point then the new points will be P’(x’, y’) given as –

Matrix Form:

**x-y Shear :**

In x-y shear, both the x and y co-ordinates changes. If P(x, y) is the point then the new points will be P’(x’, y’) given as –

Matrix Form:

**Example :**

Given a triangle with points (1, 1), (0, 0) and (1, 0).

Find out the new coordinates of the object along x-axis, y-axis, xy-axis.

(Applying shear parameter 4 on X-axis and 1 on Y-axis.).

**Explanation –**

Given, Old corner coordinates of the triangle = A (1, 1), B(0, 0), C(1, 0) Shearing parameter along X-axis (Sh_{x}) = 4 Shearing parameter along Y-axis (Sh_{y}) = 1Along x-axis:A'=(1+4*1, 1)=(5, 1) B'=(0+4*0, 0)=(0, 0) C'=(1+4*0, 0)=(1, 0)Along y-axis:A''=(1, 1+1*1)=(1, 2) B''=(0, 0+1*0)=(0, 0) C''=(1, 0+1*1)=(1, 1)Along xy-axis:A'''=(1+4*1, 1+1*1)=(5, 2) B'''=(0+4*0, 0+1*0)=(0, 0) C'''=(1+4*0, 0+1*1)=(1, 1)

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